Many optical systems incorporate aspheric optical elements to improve performance or reduce the size or number of optical elements of the systems. Most such aspheric optical elements include surfaces having finite curvatures in orthogonal directions that vary from one another or vary as a function of position. Other aspheric optical elements include finite curvatures in just one direction but the curvatures vary as a function of position. As such, the surfaces of these aspheric optical elements depart from the conventional optical forms of spheres, cylinders, and planes. Yet other aspheric optical elements include refractive indices that similarly vary with position.
Subaperture stitching techniques based on wavefront measurements have been effectively used to measure many such aspheric optical elements or similar test objects. The subapertures collectively cover the entire area of the test object intended for measurement while partially overlapping each other to provide a comparable basis for assembling the subaperture measurements into a desired full aperture measurement.
Typically, each subaperture compares a limited local area of the test object to a sphere, such as by reflecting a spherical test wavefront from the local area of the test object and comparing the reflected wavefront against the original spherical wavefront. Any departure of the local area of the test object from the referenced spherical form is incorporated into the shape of the reflected test wavefront. Various techniques are available for comparing the shape of the test wavefront against the original reference wavefront, such as by forming interference patterns, but the range of measurement over which such comparisons are effective is limited. For example, the fringe densities of interference patterns can increase beyond resolvable limits. As a result, the size of the subapertures is limited so that the local areas remain comparable to a sphere, and the number of subapertures is increased to cover the desired area of the test surface. Test objects having a form that locally departs more significantly from a spherical form can require a much larger number of subaperture measurements, which can increase measurement time, calculation complexity, noise, and other sources of error.
Certain on-axis wavefront measurements for measuring rotationally symmetric test objects stitch together a plurality of subapertures having the form of concentric annular zones. Focal distance or other adjustments are made to vary the local curvatures of the test wavefronts to match the expected curvatures of the different annular zones. In addition to incrementally varying the curvatures of reference spheres with distance along the axis of the test objects to match the nominal curvatures of different annular zones, fourth and higher order rotationally symmetric changes to the test wavefront have been proposed to match curvature variations within larger annular zones of test objects.
Although the higher order rotationally symmetric changes to the test wavefront reduce the number of measurements required to cover the desired area of a test object, the optics required for conducting these on-axis measurements must still be sized, like other on-axis measurements, in relation to the largest annular zone of the measurement. The cost of the measurement optics generally increases with size and numerical aperture, and large measurement optics can be difficult to manufacture to required accuracy. In addition, any relative change to the shape of the test wavefront beyond that imparted by the test object must be precisely known to compare the test object to the original reference wavefront. While it has been proposed to precisely measure the wavefront modifying optics along with relative motions among the optics required for imparting changes to the test wavefront, applicants have found that differences between the actual and predicted performance of the wavefront modifying optics can introduce systematic errors into the test wavefront. That is, an over-reliance on the calibration of the wavefront modifying optics can produce specious measurement results, where errors in the departure of the wavefront modifying optics from their expected form are indistinguishable from errors in the departure of the test object from its expected form.
Full aperture measurements of aspheric test objects have also been proposed using matching aspheric wavefronts. However, similar problems are apparent regarding the required size of the measuring optics and the difficulty of precisely reproducing the desired aspheric wavefronts, especially if the aspheric wavefronts must be adaptable to measuring different aspheric test objects. Such wavefront modifying optics, which can take the form of spatial light modulators, deformable mirrors, or adjustable lens assemblies, tend to be more complicated than the aspheric test objects intended for measurement, and accurate monitoring of certain dimensions of the wavefront modifying optics is no guarantee that the actual performance of the wavefront modifying optics is free of systematic errors, particularly high-order errors rendered as specious artifacts of the test object.